When a matrix A, for example 2*2 matrix, is positive defined, the following steps can compute the eigenvalues of A,
$A_k = U_k^T*U_k$
$A_{k+1} = U_k*U_k^T$
Finally, $A_k = $$ \begin{matrix} \lambda_1 & 0\\ 0 & \lambda_2 \\ \end{matrix} $ when $k = \infty$
why this procedure can reach the eigenvalues of A?